-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '324981340637301343478133211435', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [0.0, 0.0], 'a5': [-0.7050748949701935, 2.121996558075147], 'a6': [0.0, 0.0], 'a7': [0.0, 3.5671653368507146], 'a8': [0.0, 0.0], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.228331357659873, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [0.7050748949701935, -2.121996558075147]]], [13, [[1.0, 0], [3.593663649219511, 0.29254328958003273]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '780.73', 'coefficient_field': 'CDF', 'conductor': 780, 'conductor_radical': 390, 'conjugate': '2571333584669373274149601360047', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.7050748949701935, -2.121996558075147]], [[1.0, 0], [0, -3.5671653368507146], [-7.0, 0]], [[1.0, 0], [-2.9098172790319725, 2.9098172790319725], [0, -11.0]], [[1.0, 0], [3.593663649219511, 0.29254328958003273]], [[1.0, 0], [2.7413763092789956, 2.7413763092789956], [0, 17.0]], [[1.0, 0], [3.0530716075566526, -3.0530716075566526], [0, -19.0]], [[1.0, 0], [3.5863769486402948, -3.5863769486402948], [0, -23.0]], [[1.0, 0], [0, -4.286889014215215], [-29.0, 0]], [[1.0, 0], [6.4463198453954655, 6.4463198453954655], [0, 31.0]], [[1.0, 0], [0, 10.57897144809264], [-37.0, 0]], [[1.0, 0], [-5.79628478674101, -5.79628478674101], [0, 41.0]], [[1.0, 0], [7.392312074040333, -7.392312074040333], [0, -43.0]], [[1.0, 0], [0, -12.745960637516985], [-47.0, 0]], [[1.0, 0], [-6.347198322300536, -6.347198322300536], [0, 53.0]], [[1.0, 0], [3.621765359588941, 3.621765359588941], [0, 59.0]], [[1.0, 0], [-0.5591904399349349, 0], [61.0, 0]], [[1.0, 0], [9.615289478678106, 0], [67.0, 0]], [[1.0, 0], [-0.724766529629111, -0.724766529629111], [0, 71.0]], [[1.0, 0], [-3.214891458374066, 0], [73.0, 0]], [[1.0, 0], [0, -6.902520671471038], [-79.0, 0]], [[1.0, 0], [0, 4.461165767897639], [-83.0, 0]], [[1.0, 0], [6.820303325145858, 6.820303325145858], [0, 89.0]], [[1.0, 0], [12.180452412994994, 0], [97.0, 0]], [[1.0, 0], [0, 2.97899071118181], [-101.0, 0]], [[1.0, 0], [6.276607312675695, -6.276607312675695], [0, -103.0]], [[1.0, 0], [-7.533345742611787, 7.533345742611787], [0, -107.0]], [[1.0, 0], [-10.179657753161019, 10.179657753161019], [0, -109.0]], [[1.0, 0], [5.008387741478613, 5.008387741478613], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-780-65.8-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/780/2/r/a/73/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.508141658556563, 0.1617020570952551, -0.19434485328704695, -0.5604859872365485, -0.9211386740935408, -1.2417358949641693, -1.4712484086315725, -1.5494473203872225, -1.418078765873394, -1.0346703932960652, -0.3868004266430751, 0.4962582964230628, 1.5380573760133038, 2.618776038924369, 3.5899472177690215, 4.29929340240419, 4.621880767793976, 4.491053254371158, 3.921017224761149, 3.013345147994297, 1.942484202415034, 0.9203509999897331, 0.14623612213418002, -0.246158733178152, -0.22961956076212411, 0.1017020086039931, 0.5517442748065207, 0.8752050755200637, 0.8514806422426145, 0.35911813253821756, -0.5733471450291152, -1.7600387570409026, -2.9019466025017504, -3.6742878862272375, -3.8325268900386433, -3.302733833328191, -2.22298663136024, -0.915713662060708, 0.20679671208262854, 0.7770242812816839, 0.6025780692850796, -0.2554150302876857, -1.489313940111399, -2.642156492521093, -3.266225178857057, -3.088135786848475, -2.118302164974279, -0.65905458997504, 0.7982249833354004, 1.7534298603184804, 1.8886946612268662, 1.1943946631549534, -0.023780411095826813, -1.2649340002024743, -2.0360265840924248, -2.0562684717394886, -1.37623792551504, -0.3572890924413771, 0.48514966054333347, 0.7106640970705554, 0.15613770819584347, -0.9809772757578983, -2.221309635466721, -3.0150662894058016, -2.9943671341569718, -2.1505156501388036, -0.8494014543321547, 0.3297969919542884, 0.8639693382520638, 0.5391706457357964, -0.4359310326350596, -1.518684704618157, -2.090302812777357, -1.764942360092024, -0.5998082435599101, 0.9037468717194999, 2.0207674296218854, 2.147894981829077, 1.1085595113835893, -0.735560025113532, -2.631755326657119, -3.7809542750076397, -3.7169951637974994, -2.5336997223313307, -0.8427090726336887, 0.5228601509102369, 0.9148304278811876, 0.18327790144639977, -1.2621342520632577, -2.6736837483285405, -3.353988230888282, -3.007042475369052, -1.8670052041685188, -0.5392969778066478, 0.3542997994390609, 0.5255683749572141, 0.16470719355309357, -0.2057948755771986, -0.08714181883877674, 0.6376265580776962, 1.5625650891306322, 1.9381292906346639, 1.0910508148863425, -1.142946599086962, -4.226262449838604, -7.099317408230376, -8.66251621843609, -8.31450555122512, -6.256540094328979, -3.3907412780025266, -0.8598913056646458, 0.5238657775322229, 0.6497039123983356, 0.07842871902295698, -0.3594342245670412, -0.09586120824078458, 0.828270320405828, 1.8070851640894312, 2.0739145300308475, 1.2166631287417378, -0.5160650805230275, -2.3153916352674737, -3.2695626459419156, -2.9063759660099113, -1.4884055728562768, 0.12770054179266258, 0.9924335500944473, 0.6255588344167794, -0.7040270519589442, -2.154928654539008, -2.83927090064987, -2.37128890874635, -1.093750086504504, 0.16221107424922793, 0.6316899921555088, 0.12735536222913216, -0.8297550200620873, -1.3571455800672116, -0.8212232873983728, 0.6857636544376507, 2.3289123126478644, 3.0134131974572824, 2.0804128439886695, -0.22419102435011365, -2.8227826654382193, -4.401585589773889, -4.175453680637975, -2.350515664046656, 0.006477992906110241, 1.6136241946754006, 1.7312556739092348, 0.5593029194504325, -0.9636203025976103, -1.8111388160261686, -1.5344791215827633, -0.5076445924590325, 0.3937742067860168, 0.4431271056750624, -0.4143979662785382, -1.530353085762145, -2.032759470897949, -1.4765837003439946, -0.19855920286994808, 0.8895264375889156, 0.9410303452096578, -0.19518780028987748, -1.8091765927430443, -2.7729983672876055, -2.3102930347128883, -0.564927722408474, 1.4426287902336477, 2.4722048357870516, 1.906427788913511, 0.203516310363266, -1.3680001596136626, -1.5576929353342455, 0.021547226437468342, 2.603324735005905, 4.737584844811301, 5.212189427465213, 3.810766602888146, 1.4049633256427962, -0.6627324806228032, -1.4648173937999531, -1.0297077987667846, -0.18318673576707878, 0.1595122803262729, -0.2881042653304953, -0.9883719000240248, -1.0440911337545078, 0.03609946328913347, 1.8627463972000526, 3.36391306580465, 3.5384624579678152, 2.219053271195984, 0.26800764813169475, -0.9717659372431727, -0.6028164077366606, 1.183391150395491, 3.2188963585869996, 4.1614143744884835, 3.4172528313309187, 1.521844697149848, -0.293021324967233, -1.0195409126148967, -0.5948069521230862, 0.11744699259760988, 0.06983548360571687, -1.0676735534209676, -2.5494823129822937, -3.044293259028986, -1.6394015273675404, 1.3814547837134865, 4.588695234834732, 6.292940505019129, 5.656527657240661, 3.2413566002810703, 0.6027978658523331, -0.7734010631251343, -0.4263746009069355, 0.8997304708950059, 1.9321179761570668, 1.852911884601958, 0.8398684261976078, -0.21258181112283073, -0.5179830474692377, -0.07450148264105072, 0.3623109159571805, -0.017243685871789375, -1.2898440525368373, -2.6089504938695742, -2.8221773114509765, -1.4412259119359656, 0.8185001251509817, 2.419887132041031, 2.0914374632455277, -0.1753033294691124, -2.9978132539221463, -4.4978557985596765, -3.6006015461854464, -0.7921265438526435, 2.225473538118521, 3.7269903227649737, 3.123191801639056, 1.2450050946026512, -0.4116396729739847, -0.8564775564095248, -0.27700389045947293, 0.27636573023974315, -0.11626626345768383, -1.4130843312186812, -2.629690471475739, -2.6875295666925982, -1.3814819902089306, 0.3514181691595545, 1.1149274347802025, 0.1583417893907666], 'positive_zeros': ['0.25636507455507952739324993425847', '1.83992987659099892337661615664466', '3.91442385908112107545679447665243', '4.35115386069197288769152764316292', '5.17412528328823738547288994137457', '6.64165292184450564652001974583342', '7.16481957338007134098671824638883', '8.337411426793187006525270923252108', '9.137457532429043709982418380128021', '10.08409333343925758445279148047861'], 'prelabel': '2-780-65.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4956625087659337, 'root_angle': -0.8522416450997435, 'root_number': '-0.8941815568832506 - 0.4477045268141098*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.42612082255', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25636507455507952739324993426', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83992987659099892337661615664', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.91442385908112107545679447665', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 6.228331357659873, 'bad_primes': [2, 3, 5, 13], 'central_character': '65.8', 'conductor': 780, 'conductor_radical': 390, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/780/2/r/a/73/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-780-65.8-c1-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-780-65.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4956625087659337, 'root_angle': -0.42612082254987177, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.25636507455507952739324993426', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '324981340637301343478133211435', 'Lhash_array': ['324981340637301343478133211435'], 'label': '2-780-65.8-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/780/2/r/a/73/3'}